Year: 2024
Type: preprint
Abstract: In this article, we introduce an exponential for tropical matrices and show that this series is essential for the analysis of certain kinds of stability in discrete event dynamic systems. A notion of a generalised eigenvector is introduced to discuss this kind of stability and prove it exists at most in the order of $1,p/2,p$, where $p$ is the period of the corresponding matrix. Thus characterizing the generalised eigenvectors of all powers of the matrix. Also, a sufficient condition is proved for the exponential of a matrix to be robust.
Source: arXiv (Cornell University)
Authors: M, Askar Ali, Mukherjee, Himadri
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4401202062